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A candy-filled piñata is hung from a tree for Matthew's birthday. During an unsuccessful attempt to break the 4.4-kg piñata, Hayden cracks it with a 0.54-kg stick moving at 4.8 m/s. The stick stops and the piñata undergoes a gentle swinging motion. Determine the swing speed of the piñata immediately after being cracked by the stick.

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whitneytr12

Answer:

The speed of the piñata immediately after being cracked by the stick is [tex]v_{fp}=0.59\: m/s[/tex].

Explanation:

Using the conservation of linear momentum:

[tex]m_{s}v_{is}=m_{p}v_{fp}[/tex] (1)

Here:

m(s) is the mass of the stick

m(p) is the mass of the piñata

v(is) is the initial velocity of the stick

v(fp) is the final velocity of the piñata        

So, we just need to solve the equation (1) to v(fp).

[tex]v_{fp}=\frac{m_{s}v_{is}}{m_{p}}[/tex]

[tex]v_{fp}=\frac{0.54*4.8}{4.4}[/tex]

[tex]v_{fp}=0.59\: m/s[/tex]

I hope it helps you!

Lanuel

The swing speed of the piñata immediately after being cracked by the stick is 0.59 m/s.

Given the following data:

  • Mass of piñata = 4.4 kg
  • Mass of stick = 0.54 kg
  • Velocity of stick = 4.8 m/s

To find the swing speed of the piñata immediately after being cracked by the stick, we would apply the law of conservation of momentum:

The law of conservation of momentum states that the total linear momentum of any closed system would always remain constant with respect to time.

Hence, the total linear momentum of two objects before collision is equal to the total linear momentum of the objects after collision.

Mathematically, this is given by the formula:

[tex]M_SU_S = M_PV_P[/tex]

Where;

  • Ms is the mass of the stick.
  • Us is the initial velocity of the stick.
  • Mp is the mass of piñata.
  • Vp is the final velocity of the piñata.

Making Vp the subject of formula, we have:

[tex]V_P = \frac{M_SU_S}{M_P}[/tex]

Substituting the given parameters into the formula, we have;

[tex]V_P = \frac{0.54(4.8)}{4.4}\\\\V_P = \frac{2.592}{4.4}[/tex]

Vp = 0.59 m/s.

Read more: https://brainly.com/question/20693852

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